Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness

Josef Dick; Aicke Hinrichs; Lev Markhasin; Friedrich Pillichshammer

doi:10.1112/S0025579317000213

Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness

Josef Dick
, Aicke Hinrichs
, Lev Markhasin
, Friedrich Pillichshammer

Research output: Contribution to journal › Article › peer-review

Abstract

The discrepancy function measures the deviation of the empirical distribution of a point set in $[0,1]^d$ from the uniform distribution. In this paper, we study the classical discrepancy function with respect to the bounded mean oscillation and exponential Orlicz norms, as well as Sobolev, Besov and Triebel–Lizorkin norms with dominating mixed smoothness. We give sharp bounds for the discrepancy function under such norms with respect to infinite sequences.

Original language	English
Pages (from-to)	863-894
Number of pages	32
Journal	Mathematika
Volume	63
Issue number	3
DOIs	https://doi.org/10.1112/S0025579317000213
Publication status	Published - 2017

Fields of science

101 Mathematics
101002 Analysis
101007 Financial mathematics
101019 Stochastics
101025 Number theory
101032 Functional analysis

JKU Focus areas

Computation in Informatics and Mathematics

Access to Document

10.1112/S0025579317000213

Cite this

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title = "Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness",

abstract = "The discrepancy function measures the deviation of the empirical distribution of a point set in \$[0,1]\textasciicircum{}d\$ from the uniform distribution. In this paper, we study the classical discrepancy function with respect to the bounded mean oscillation and exponential Orlicz norms, as well as Sobolev, Besov and Triebel–Lizorkin norms with dominating mixed smoothness. We give sharp bounds for the discrepancy function under such norms with respect to infinite sequences.",

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AU - Markhasin, Lev

AU - Pillichshammer, Friedrich

PY - 2017

Y1 - 2017

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AB - The discrepancy function measures the deviation of the empirical distribution of a point set in $[0,1]^d$ from the uniform distribution. In this paper, we study the classical discrepancy function with respect to the bounded mean oscillation and exponential Orlicz norms, as well as Sobolev, Besov and Triebel–Lizorkin norms with dominating mixed smoothness. We give sharp bounds for the discrepancy function under such norms with respect to infinite sequences.

U2 - 10.1112/S0025579317000213

DO - 10.1112/S0025579317000213

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JO - Mathematika

JF - Mathematika

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